With the tagline “healthy living with a twist,” the soon-to-be-launched Lime network is eyeing a big slice of the growing market for eco-friendly, healthconscious consumers.

Lime – part of AOL cofounder Steve Case’s health and wellness investment company – aspires to be the first multimedia brand devoted to, in its own words, a “new generation that naturally gravitates toward green.”

After emerging from the merger of AOL and Time Warner, Case, armed with at least $500 million of his own money, is investing in companies that help people take care of themselves.

Lime is the reincarnation of Wisdom Media, whose cable and radio networks were also geared toward a greener lifestyle but didn’t gain much traction. Case’s company, Revolution, acquired those assets earlier this year.

The Lime name and wedge-shaped logo will be spread across several businesses, including a cable network, a 24-hour radio channel on Sirius Satellite Radio, and a Web site. The brand is intended to reflect a hipper, more sophisticated sensibility, while steering clear of New Age notions involving, say, granola or healing crystals.

The potential for advertisers seeking to sell products ranging from hybrid cars to organic food is huge, with spending estimated at $230 billion annually.